Pursuit Differential Game of Many Pursuers with Integral Constraints on Compact Convex Set

被引：6

作者：

Ferrara, Massimiliano ^{[1
,2
,3
]}

Ibragimov, Gafurjan ^{[4
,5
]}

Alias, Idham Arif ^{[4
,5
]}

Salimi, Mehdi ^{[1
,2
,6
]}

机构：

[1] Univ Mediterranea Reggio Calabria, Dept Law Econ & Human Sci, I-89125 Reggio Di Calabria, Italy

[2] Univ Mediterranea Reggio Calabria, Decis Lab, I-89125 Reggio Di Calabria, Italy

[3] Bocconi Univ, ICRIOS Invernizzi Ctr Res Innovat Org Strategy &, I-20136 Milan, Italy

[4] Univ Putra Malaysia, Dept Math, Serdang, Malaysia

[5] Univ Putra Malaysia, Inst Math Res, Serdang, Malaysia

[6] Tech Univ Dresden, Ctr Dynam, Dept Math, D-01062 Dresden, Germany

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2020年 / 43卷 / 04期

关键词：

Differential game; Control; Strategy; Integral constraint; State constraint; Primary: 91A23; Secondary: 49N75; EVASION; EVADERS;

D O I：

10.1007/s40840-019-00844-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study a pursuit differential game of many pursuers and one evader in the plane. We are given a compact convex subset of R2, and the pursuers and evader move in this set. They cannot leave this set during the game. Control functions of players are subject to coordinate-wise integral constraints. If the state of a pursuer coincides with that of evader at some time, then we say that pursuit is completed. Pursuers try to complete the pursuit, and the aim of the evader is opposite. We obtain some conditions under which pursuit can be completed from any positions of the players in the given set. Moreover, we construct strategies for the pursuers. Also, we prove some properties of convex sets.

引用

页码：2929 / 2950

页数：22

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